How many times do you think you used  the "th"  sound in conversation?  

​The "Th" sound is a pretty important sound.  

I think you would agree after reading why. 
Importance in a Nutshell:
1) It is the most commonly occurring consonant sound in English.  Think about it...the word "the".  It is an article, and we use them quite a bit.  /Th/ is also found in pronouns.  How often do we use pronouns? Again- A lot!  
2) If it isn't produced correctly, it can become a different word.  This can make things get confusing and/or uncomfortable for not only you as the speaker but the listener.  Have you ever stood there wondering what the other person said and didn't want to ask the umpteenth time?   Better yet, what about when you spoke to your OWN family and discovered you weren't used to their accent anymore.  You can't believe you don't understand your own parents because you have been away too long. What?!! Yes, that has happened.
3. The sound is not in many other languages. 
​When that happens, you might substitute it for another sound. 

How to Produce /TH/

• Breathe in and stick the tip of your tongue between your front teeth
• Make sure your tongue tip is up against your top teeth-anchoring it in place
• Let the air come out

Watch the video for word and sentence practice:
in and stick the tip of your tongue between your teeth

 
"Why can't I make this sound right?"

“Why does it sound different from how she is saying it?”

Or possibly frustrated that you don’t know how to change a consonant sound to be closer to what a native speaker says it. 

It is because consonants are produced differently in American English or the General American accent.

Some consonant sounds don't even exist in other languages.  

One way to look and analyze how to correctly make a consonant sound is by analyzing the place, manner, and voicing of a consonant. This is what professionals, such as me, utilize to analyze the difference of how a consonant is produced vs how a speaker is producing the sound. 

Place: This pertains to where the sound is produced.
Is it produced using both your lips?  Is the sound produced by placing your tongue behind your teeth, which is called the alveolar ridge (e.g., /t/). There are eight different categories.
 
Manner: This pertains to how the sound is produced.
Are you stopping the sound and then have a burst (e.g., /t, d, k, g)? There are six areas on how a sound is produced.

Voicing: This pertains to whether your voice is "on" or "off". This refers to whether you are using vocal folds or not to produce the sound. With voice sounds, your vocal folds are vibrating. Consonants are voiceless or voiced consonants.  You know you are using your voice when you place your hand on your throat and feel if it is vibrating.  Voiced consonant sounds include some of the following: /b, d, g, v, ð, z/.

Would I say it is necessary to know ALL details for all three areas to produce consonants correctly? 
 
I would say no, because it might get confusing and more information that you don’t necessarily need to know to learn a sound.
 
It is important to know place and manner (and voicing depending on the sound) of the sound you are focusing on. You can find out on your own, of course, but also can seek out the expertise of a professional or someone knowledgeable to only focus on information that is necessary to know and leave out anything that is unnecessary.

If you have already started accent training sessions, this way of analyzing sounds can be helpful troubleshooting between sessions as well.  If you just learned the sound and find that it still doesn’t sound close to the American English pronunciation, you can think where exactly the breakdown is and it discuss it with your accent instructor or coach.  For example, are you cutting off the sound too quickly making a "th" sound more like a /t,d/? Do you have your voice off instead of on? 
 
If you would like a more in-depth description and nitty gritty of each area, let me know in the comments.  
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 Have you ever heard of the place-manner-voicing analysis?